Our review of capital market history showed that the returns to investors have varied according to the risks they have borne. At one extreme, very safe securities like U.S. Treasury bills have provided an average return over 109 years of only 4.0% a year. The riskiest securities that we looked at were common stocks. The stock market provided an average return of 11.1%, a premium of 7.1% over the safe rate of interest.

This gives us two benchmarks for the opportunity cost of capital. If we are evaluating a safe project, we discount at the current risk-free rate of interest. If we are evaluating a project of average risk, we discount at the expected return on the average common stock. Historical evidence suggests that this return is 7.1% above the risk-free rate, but many financial managers and economists opt for a lower figure. That still leaves us with a lot of assets that don't fit these simple cases. Before we can deal with them, we need to learn how to measure risk.

Risk is best judged in a portfolio context. Most investors do not put all their eggs into one basket: They diversify. Thus the effective risk of any security cannot be judged by an examination of that security alone. Part of the uncertainty about the security's return is diversified away when the security is grouped with others in a portfolio.

Risk in investment means that future returns are unpredictable. This spread of possible outcomes is usually measured by standard deviation. The standard deviation of the market portfolio, generally represented by the Standard and Poor's Composite Index, is around 15% to 20% a year.

Most individual stocks have higher standard deviations than this, but much of their variability represents specific risk that can be eliminated by diversification. Diversification cannot eliminate market risk. Diversified portfolios are exposed to variation in the general level of the market.

A security's contribution to the risk of a well-diversified portfolio depends on how the security is liable to be affected by a general market decline. This sensitivity to market movements is known as beta (β). Beta measures the amount that investors expect the stock price to change for each additional 1% change in the market. The average beta of all stocks is 1.0. A stock with a beta greater than 1 is unusually sensitive to market movements; a stock with a beta below 1 is unusually insensitive to market movements. The standard deviation of a well-diversified portfolio is proportional to its beta. Thus a diversified portfolio invested in stocks with a beta of 2.0 will have twice the risk of a diversified portfolio with a beta of 1.0.

One theme of this chapter is that diversification is a good thing for the investor. This does not imply that firms should diversify. Corporate diversification is redundant if investors can diversify on their own account. Since diversification does not affect the value of the firm, present values add even when risk is explicitly considered. Thanks to value additivity, the net present value rule for capital budgeting works even under uncertainty.

In this chapter we have introduced you to a number of formulas. They are reproduced in the endpapers to the book. You should take a look and check that you understand them.

Near the end of Chapter 9 we list some Excel functions that are useful for measuring the risk of stocks and portfolios.